I'll try it your way for once

Complete all missions on Vergil's Downfall on the Nephilim difficulty with a SSS rank.

The Nephilim difficulty is the hardest of the first three starting difficulties. An SSS rank is earned by earning many Style Points, completing the mission under a certain time limit, finding all Collectibles, and not dying or using many items. See Style Ranks for more info.

You might also want to wait until you've upgraded Vergil's devil trigger gauge to maximum as using Spiral Swords is the easiest way to attain a Sensational rank in combat. Completing each mission on this difficulty with an SSS Rank to earn this achievement / trophy.